The fractal modelling of turbulent surface-layer winds

by Lauren, Michael Kyle

Abstract (Summary)

Multiscaling analysis and cascade simulation techniques, which form part of the more general field of fractals, are introduced as a method for characterising and simulating surface-layer winds, particularly for time scales associated with the energy-containing range. This type of analysis consists of determining the power-law parameter of the spectrum of the data, and the scaling of the statistical moments. These techniques were applied to determine how the statistics depended on the duration (or scale) of the fluctuations in wind speed, the atmospheric conditions, and the topography of the site. It was found that the parameterisations produced using multiscaling analysis characterised differences in the statistics for each of these cases. Furthermore, the fractal cascade simulation techniques used provided simple methods for reproducing these statistics. This analysis is followed by an investigation into the robustness of some of these results. In particular, the data is examined for the existence of self-similar distributions of the cascade weighting factor, W. Such self-similar analysis allows the direct simulation of the data via a cascade. Cascade models have the virtue of being able to reproduce statistical properties such as intermittency, and in particular, the nesting of intermittency from different wavenumber bands in the same region of space. The existence of these properties in both the experimental and simulated data is investigated, with consideration given to the consequence of the results for simulation techniques. One notable discovery is the failure of these methods to reproduce the bias in the distribution of the gradients in the wind velocity field. This result has important implications for all workers dealing with simulation of geophysical data by fractal cascades. Finally, a brief numerical experiment is carried out to both demonstrate how this bias may be exploited to construct a model, and to test some of the analysis techniques presented on non-cascade based data. While not a particularly convincing simulator of turbulence, the model nevertheless displays some interesting turbulence-like characteristics.